A fireman, 34.9 m away from a burning
building, directs a stream jet of water from a ground level fire hose at an angle of 44.2◦ above the horizontal. If the speed of the stream as it leaves the
hose is 60.5 m/s, at what height will the stream of water strike the building? The acceleration due to gravity is 9.8 m/s^2
Answer in units of m.
To find the height at which the stream of water will strike the building, we can use the principles of projectile motion.
First, let's break down the motion of the water stream into its horizontal and vertical components. The horizontal component remains constant, while the vertical component is affected by gravity.
The initial velocity of the water stream can be split into its horizontal and vertical components as follows:
Vx = V * cos(θ)
Vy = V * sin(θ)
where Vx is the horizontal component, Vy is the vertical component, V is the initial velocity of the water stream (60.5 m/s), and θ is the angle of elevation (44.2°).
Now, let's calculate the time it takes for the water stream to reach the building. We'll use the equation:
t = d / Vx
where d is the horizontal distance between the fireman and the building (34.9 m) and Vx is the horizontal component of the initial velocity.
Substituting the values, we get:
t = 34.9 / (60.5 * cos(44.2°))
Next, let's find the height the water stream will travel in this time. We'll use the equation:
y = Vy * t - (1/2) * g * t^2
where y is the height, Vy is the vertical component of the initial velocity, t is the time, and g is the acceleration due to gravity (9.8 m/s²).
Substituting the values, we get:
y = (60.5 * sin(44.2°)) * t - (1/2) * (9.8) * t^2
Now we can calculate the height.